Resumen:
Given a set S of points in the two-dimensional space, which are stored
in a spatial database, this paper presents an e cient algorithm to nd the empty
circle, in the area delimited by those points, with the largest area and containing
only a query point q.
Our algorithm adapts previous work in the eld of computational geometry to
be used in spatial databases, which require to manage large amounts of data. To
achieve this objective, the basic idea is to discard a large part of the points of S,
in such a way that the problem can be solved providing only the remaining points
to a classical computational geometry algorithm that, by processing a smaller
collection of points, saves main memory resources and computation time.
The correctness of our algorithm is formally proven. In addition, we empirically
show its e ciency and scalability by running a set of experiments using both
synthetic and real data.
